Signatures of the many-body localized regime in two dimensions

Abstract

Lessons from Anderson localization highlight the importance of dimensionality of real space for localization due to disorder. More recently, studies of many-body localization have focussed on the phenomenon in one dimension using techniques of exact diagonalization and tensor networks. On the other hand, experiments in two dimensions have provided concrete results going beyond the previously numerically accessible limits while posing several challenging questions. We present the first large-scale numerical examination of a disordered Bose-Hubbard model in two dimensions realized in cold atoms, which shows entanglement based signatures of many-body localization. By generalizing a low-depth quantum circuit to two dimensions we approximate eigenstates in the experimental parameter regimes for large systems, which is beyond the scope of exact diagonalization. A careful analysis of the eigenstate entanglement structure provides an indication of the putative phase transition marked by a peak in the fluctuations of entanglement entropy in a parameter range consistent with experiments.Many-body localization (MBL) is a paradigm shift in out-of-equilibrium quantum matter. This novel phase of matter is characterized by the absence of thermalization 1-6 . An MBL system retains a memory of its initial state and displays only a logarithmic growth of entanglement following quantum quenches 7 . By localizing the excitations, MBL can also protect certain forms of topological and symmetry-breaking orders in excited states and provides an opportunity to process quantum information in a system driven far from equilibrium 8-11 . The quantum phase transition separating the MBL and thermal phases poses a major challenge for developing a theory of dynamical critical phenomena described by manybody entanglement in highly excited states 12-18 .It is well-known that dimensionality of real space affects single particle Anderson localization where in one and two dimensions (without spin-orbit coupling and broken time-reversal symmetry), the entire spectrum of single particle eigenstates is localized for arbitrarily weak disorder 19 . Although the defining properties of MBL in one dimension are firmly established both theoretically and experimentally 20,21 , the existence of the phenomenon in two and higher dimensions is much debated 22-28 . Experiments in cold atoms measuring local and global equilibration have shown the persistence of quantum memory for long times providing indications of an MBL-like phase in two dimensions 28-30 . On the other hand, theoretical criteria suggest that the lifetime of local memory is finite, albeit extremely long 22,23 .In this article, we evaluate the eigenstates of bosons hopping in a disordered lattice in two dimensions with on-site interactions. We generalize the tensor network method developed earlier for one dimensional systems to approximate the eigenstates in the localized regime 31 .Because the system sizes accessible by our method are much larger than those that can be currently achieved with prior ...

Two-body mobility edge in the Anderson-Hubbard model in three dimensions: Molecular versus scattering states

“…Analytical arguments were given [47,48] suggesting that the many-body localized phase in the thermodynamic limit is inherently unstable against the formation of thermal bubbles. This prediction contrasts with numerical investigations of two-dimensional disordered Hubbard models [49,50], providing evidence for a manybody localized phase at strong disorder. Similar conclusions have also been reached for 2D models of spinless fermions with nearest-neighbor interactions [51,52] and of quantum dimers [53].…”

Many-body localization as a large family of localized ground states

“…An interesting continuation of this work would be to extend it to higher dimensions, although more numerically challenging. In particular, we believe that it would allow one to tackle the MBL phenomena in two dimensions where only a few theoretical studies are available [67][68][69][70][71], despite a recent experimental observation [72].…”

Colloquium : Many-body localization, thermalization, and entanglement

“…At the same time, the new numerical tools are essential for describing 1d systems with local Hilbert space larger than 2 (bosons, spinful fermions, higher spins) and for studies of phase transitions between MBL and thermal phases, as well as between different MBL phases. Finally, the development of tensor-network methods for excited states is necessary for investigating MBL in higher dimensions (Wahl et al, 2017), which is also the subject of current experimental studies, see Section V.…”